Math Problem Statement

Use the given table of the function c(p) to determine the answers to the following questions: a) Vertical Intercept, b) Horizontal Intercept, c) Evaluate c(2), d) Solve c(p) = -3.

Solution

From the image, we have a table that provides values of pp and corresponding values of the function c(p)c(p). There are also four questions to be answered based on this table. Let's go over each question and provide the answers.

Table Data:

ppc(p)c(p)
-21
-10
0-2
1-3
2-1

Questions:

  1. (a) Vertical Intercept
    The vertical intercept occurs when p=0p = 0. From the table, c(0)=2c(0) = -2.
    Answer: The vertical intercept is (0,2)(0, -2).

  2. (b) Horizontal Intercept
    The horizontal intercept occurs when c(p)=0c(p) = 0. From the table, c(1)=0c(-1) = 0.
    Answer: The horizontal intercept is (1,0)(-1, 0).

  3. (c) Evaluate c(2)c(2)
    From the table, c(2)=1c(2) = -1.
    Answer: c(2)=1c(2) = -1.

  4. (d) Solve c(p)=3c(p) = -3
    From the table, c(1)=3c(1) = -3.
    Answer: p=1p = 1 solves c(p)=3c(p) = -3.

Would you like more details or have any other questions?

Here are 5 related questions that you could explore further:

  1. What is the slope of the function between p=1p = -1 and p=0p = 0?
  2. What is the average rate of change of the function between p=2p = -2 and p=2p = 2?
  3. Can you find a linear equation that might approximate the function based on the given points?
  4. How would the graph of this function look based on the table?
  5. Is the function increasing or decreasing between p=2p = -2 and p=2p = 2?

Tip: The vertical and horizontal intercepts are crucial when sketching the graph of a function, as they give important clues about where the function crosses the axes.

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Math Problem Analysis

Mathematical Concepts

Functions
Intercepts
Evaluation
Solving equations

Formulas

Vertical Intercept: Set p = 0, Horizontal Intercept: Set c(p) = 0

Theorems

None directly involved

Suitable Grade Level

Grades 9-11